Second sound measurement of absolute rotational motion

ABSTRACT

A method and apparatus for measuring absolute rotational motion by producing entropy waves in liquid helium II filling a cylindrical container rotationally mounted with respect to a fixed reference. A carbon resistance heater generates an entropy wave beam to a beam splitter where it is divided into two beams progressing oppositely through the liquid helium II at a speed independent of the angular velocity of the container. Reflectors attached to the container reflect the two oppositely directed beams to a detector station where the sense and magnitude of any phase difference between the beams actuates a phase detector. The phase detector produces a signal proportional to the sense and magnitude of the phase difference to a servo loop coupled to adjust the rotational motion of the container.

United States Patent Inventor Donald L. Ensley San Leandro. Calif Appl.No. "9,133

Filed Apr. 5, 1968 Patented Aug. 3, I971 Assignee Ihrvest Queen Mill 8:Elevator Co.

Dallas, Tex.

SECOND SOUND MEASUREMENT OF ABSOLUTE ROTATIONAL MOTION 16 Claims, 2Drawing Figs.

u.s. Cl 73/505 601p 3/00 Field of Search 73/505 References Cited UNITED.STATES PATENTS 3.395.270 7/l968 Speller 73/505 X Primary Examiner-James.l. Gill Attorney-Richards. Harris 8: Hubbard ABSTRACT: A method andapparatus for measuring absolute rotational motion by producing entropywaves in liquid helium ll filling a cylindrical container rotationallymounted with respect to a fixed reference. A carbon resistance heatergenerates an entropy wave beam to a beam splitter where it is dividedinto two beams progressing oppositely through the liquid helium II at aspeed independent of the angular velocity of the container. Reflectorsattached to the container reflect the two oppositely directed beams to adetector station where the sense and magnitude of any phase differencebetween the beams actuates a phase detector. The phase detector producesa signal proportional to the sense and magnitude of the phase differenceto a servo loop coupled to adjust the rotational motion of thecontainer.

ATENIEH AUG 3 I9?! SERVO R O T N E V W DONALD LUTHER ENSLE Y FIG.

W Wanna 9 fi m ATTORNEY EECOND fitlllUNlll MEASUREMENT Oli AllilSOiUUTElliOTA'llllUhlAlL MOTIIOW BACKGROUND OF THE lN'VENTlON This inventionrelates to the measurement of absolute rotational motion, and moreparticularly to the measurement of absolute rotational motion by meansof entropy waves generated in liquid helium ll.

in sensing motion such as displacement, velocity or acceleration,various systems have been devised for generating electrical functionswhich are dependent in magnitude on the character of the motion and arekeyed in dependence upon the direction or sense of the motion. Suchsystems usually employ a supported mass as a reference element forindicating relative motion. Various light radiating and optical systemshave been provided for measuring the sense and magnitude of therotational motion of the supported mass. Typical of such systems is onewherein polarized light passes through a housing moving relative to thesupported mass and is then focused on a light responsive device.

A type of ring laser has also been described as a method of detectingabsolute rotational motion. However, such systems lack accuracy due tolow sensitivity and instability against dimensional change.

in accordance with the present invention, absolute rotational motion ismeasured by means of an entropy wave transmitted through liquid heliumll maintained at a temperature on the order of K. to 2.2 it. The entropywaves are generated by a heater centrally located within the liquidhelium I] bath. A beam splitter divides the entropy wave into two beamsdirected oppositely through the liquid helium II to a detector station.Any relative angular motion of the sourcereceiver system, with respectto the liquid helium ll, causes a change in phase displacement betweenthe two oppositely directed beams at the receiver relative to the phaseshift when no angular motion is present. This phase difference isdirectly proportional to the angular velocity of the system relative tothe at rest condition at a given temperature.

In a more specific aspect of the invention, a cylindrical container isrotationally mounted with respect to a fixed reference and containsliquid helium ll maintained at a temperature of about 1.5 if. Aresistance heater is energized from a 100 kHz. source and generates anentropy wave beam to a beam splitter where it is divided into twooppositely directed beams. The beam splitter is attached to thecontainer walls. Reflectors, also attached to the container walls,reflect the oppositely directed beams to a detector station wherethermocouple devices respond to the sense and magnitude of a phasedifference between the oppositely directed beams. A signal generated atthe detector station is amplified in a servo loop coupled to adjust therotational motion of the cylindrical container. The motion of thecontainer is adjusted to maintain a null or zero phase shift between thetwo oppositely directed beams.

It is a primary object of the present invention to provide a measuringsystem of absolute rotational motion free from diffusion effects ofoptical sensing systems. A further object of the invention is to providea measurement of absolute rotational motion by means of entropy wavespropagating through liquid helium ll. it is a further object of theinvention to provide a measurement of absolute rotational motion whereinan entropy wave beam is split into two beams oppositely directed toproduce a phase difference proportional to angular motion.

SUMMARY As set forth in the appended claims, this invention relates to amotion transducer wherein an entropy wave is generated in a superfluidbath and split into two oppositely directed beams. A signal proportionalto the sense and magnitude of the phase difference between the twooppositely directed beams is generated at a detector station by phaseresponsive means.

A more complete understanding of the invention and its advantages willbe apparent from the specification and claims and from the accompanyingdrawings illustrative of the invention.

BRIEF DESCRIPTlON OF THE DRAWINGS FIG. 1 schematically illustrates thetop view of a system for measuring absolute rotational motion; and

HO. 2 is an isometric view illustrating schematically the system shownin FllG. 11.

DESCRIPTION OF THE PREFERRED EMBODIMENT Referring to FIG. ll,measurement of absolute rotational motion is provided for by means of acylindrical container 110 rotationally mounted with respect to a fixedreference surface 12, such as a space vehicle. A followup servo link 14coupled to the output of a servo lib controls the angular velocity ofthe container ill with respect to the reference 12. A carbon resistanceheater 11b, centrally located within the container it], ans surroundedby a shield 20, generates an entropy wave directed to the containerwalls. This heater lid is energized from an oscillator 22 at a frequencyon the order of about kll llz. An entropy wave propagating from theheater i8 is split into two oppositely directed beams by a beam splitter2d attached to the inner wall of the container 10. In the top view ofFIG. ll, only the clockwise directed beam is shown. After reflectionfrom the beam splitter 2A0, the clockwise directed beam is furtherreflected by means of a mirror 26 to a phase summing point 2%. From thephase summing point 2%, the clockwise directed beam passes from thecontainer through a window 30 to be dissipated in an energy absorber(not shown). The container W is filled with a superfluid such as liquidhelium II through which the entropy wave is transmitted. I

Superfluid helium, also known as liquid helium II, at temperatures belowabout 2.2 K. exhibits properties which are different from any knownsolid, liquid, or gas. Because of its peculiar behavior, liquid heliumII has been said to be the only representative of a fourth state whichcannot be identified with either the solid, liquid or gaseous states.Above a temperature of about 2.2 ll(., known as the lambda transitionpoint, liquid helium behaves like any normal low temperature liquid.Below the lambda point, however, superfluid helium behaves in a veryabnormal way which cannot be described using normal definitions ofviscosity and thermal conductivity. Because of this peculiar behavior,the properties of superfluid helium are defined by what is known as thetwo fluid theory." Under the two fluid theory," the density of liquidhelium II may be divided into two parts:

P=Pl+pn where p, is the superfiuid component which has a negligibleviscosity and p is the normal component associated with a normal typeviscosity. One of the most peculiar properties of superfluid helium isthe negligible viscosity of the superfluid component which flows readilythrough very small passages on the order of about 10 centimeters.

Another peculiarity of liquid helium II, and probably the mostinteresting, is the ability of the liquid to propagate two differenttypes of waves. These are first sound, or ordinary sound, in which thesuperfluid and normal components move in phase with one another, andsecond sound in which the two components vibrate with a phase differenceof 180. Second sound is a temperature or entropy wave where thesuperfluid component collects at a point of low temperature while thenormal component collects at a point of high temperature half awavelength away. Second sound can be generated by periodic energizing aheating element just as first sound can be excited by periodiccompression of the liquid. The periodic energization of a heatingelement produces temperature variations in the liquid which propagatesas an entropy wave.

The kinetic energy of the internal convection heat waves can be by theequation:

il P where v, is the velocity of the superfluid component and v,, is thevelocity of the normal component. ln superfluid helium, the normalcomponent propagates the heat wave in one direction and the superfluidcomponent occurs in a counterflow direction. thus p,,v,,=-p,v,, With aperiodic heat flux as generated by energizing the heater 18 the heatcurrent is given by the equation:

P-"3" 3 l where s is the entropy per gram of liquid helium, and T is thebath temperature in degrees Kelvin. From the above, it can be readilyshown that the characteristic velocity of a second sound of thermal wavein z =(p./p,.)'(sT/c,.) where c, is the specific heat of the liquidhelium at a constant pressure.

The operation of the system of this invention is based primarily uponstill another peculiar property of liquid helium ll; that is, thevelocity of the superfluid component remains near zero below someidentifiable critical velocity of the container 10. Below the A pointtransition temperature and below the critical velocity, a finitefraction of helium atoms fall into a single coherent state; thisfraction increases from zero at the point temperature to unit at K. Withhelium atoms in the single coherent state, the container 10 can berotated without imparting motion to the superfluid component of theliquid helium bath. ln other words, the superfluid component of theliquid helium ll remains at rest so long as the container 10 rotates atan angular velocity below the critical velocity. Under these conditions,it can be said that the liquid helium ll has zero coupling.

The angular motion of the superfluid component of liquid helium ll belowthe A point temperature takes place as quantized vortex motion as givenby the expression:

7,, dl=n(21fii/m) (5) where i is Planks constant over Zn, in is the restmass of the helium atom (isotope H V, is the average value of thesuperfluid component velocity, and n is an integer, which is the quantumnumber associated with the angular degree of freedom. For a cylinder offluid such as container 10, the velocity of the superfluid component atany selected distance from the axis is given by:

v,,=rT/mr l (6) where r is any selected radius. The angular momentum ofthe superfluid component is quantized and its quantum step given by theexpression:

where p, is the density of the superfluid component.

Before motion of the superfluid component can occur, the cylinder 10must rotate at an angular velocity above the critical value. Thiscritical angular velocity is given by the equation:

w.= ?p./1p (8) where l is the effective moment of inertia of the bath ofliquid helium ll, N is the total number of He atoms/cm, and p is themass density of the liquid helium ll. According to the equation (8),below the critical angular velocity, (0,, the liquid helium bathconsists of a superfluid component which is entirely at rest. This meansthat for any angular velocity smaller than the critical velocity, thesuperfluid component of the liquid helium ll does not move with thecontainer 10.

Referring to FIG. 1, as a typical example, the container 10 includes 500cm of liquid helium ll which has an at rest mass of 70 grams, and aneffective moment of inertia of 5X10 grams-cm of the container 10 is onthe order of 60 per hour. For such a system, the time constant of servo16 must be maintained below the 60 per hour figure.

Referring to H0. 2, there is shown both the clockwise andcounterclockwise entropy beams. The resistance heater 18 within theshield 20 generates an entropy wave to the beam splitter sections 24aand 24b to be split into two oppositely directed beams as describedpreviously. In the upper section of the container 10, the entropy beamis directed in a clockwise direction and reflected from the mirror 26 tothe phase summing point 28. At the lower portion of the container 10 acounterclockwise beam is propagated through the liquid helium andreflected from a mirror 32 to a phase summing point 34. After reflectionfrom the summing point 28, the clockwise beam passes out of thecontainer 10 through a window l0 and the counterclockwise beam isdirected from the container through a window 36.

The phase summing points 28 and 34 comprise a detector station and areresponsive to the sense and magnitude of the temperature waves impingingthereon and generate an input signal to a phase sensitive amplifier 38.The amplifier 38 in turn generates a servo input signal proportional tothe sense and magnitude of the phase difference between the twooppositely directed beams propagated through the liquid helium ll. Thissignal connects to the drive of the servo 16.

in the absence of rotation of the container 10, the time required forthe oppositely directed beams to travel from the beam splitter 24 to therespective phase summing points 28 and 34 is given by the expression:

M O/ Z where d is the distance from the beam splitter 24 to the phasesumming points, and a is the velocity of propagation of the temperaturewave as given by equation 4. With rotation of the container 10 withrespect to the liquid helium bath, that is, when the angular velocity isbelow the critical value, the travel time for the beams is given by theexpression:

( Y Mn/ r a where m is the rotation rate of the container relative tothe liquid helium. In the above expression, the plus sign identifies theclockwise wave time and the minus sign the counterclockwise wave timefor clockwise rotation of the container 10. The time difference for thetwo waves to reach the detector station is then equal to:

where A is the area enclosed by the container 10. From this expressionone can write an equation for the phase difference between the two wavesas follows:

A 1 =(Aw/)t 14 (12) where A is the wavelength of the temperature wave.This phase difference is directly proportional to the angular velocityof the container 10 relative to the absolute rest position of thesuperfluid component of the liquid helium ll. So long as the angularvelocity of the container 10 remains below the critical value, thisexpression holds true.

The signal from the phase sensing amplifier 38, as given by the aboveexpression, drives the servo 16 to maintain the angular velocity of thecontainer 10 at a minimum value, thus nulling the difference between thetwo oppositely directed beams.

While only one embodiment of the invention, together with modificationsthereof, has been described in detail herein and shown in theaccompanying drawings, it will be evident that various furthermodifications are possible in the arrangement and construction withoutdeparting from the scope of the invention.

What I claim is:

l. A motion transducer comprising:

a superfluid bath within a housing positionable with respect to a fixedreference, said bath having a superfluid component that remains at restbelow a critical velocity of said housing,

generator means for producing high frequency entropy waves in said bath,

reflector means for splitting said waves into two beams oppositelydirected through said bath, such that with the housing in an at restposition with respect to the fixed reference, both beams travelsubstantially an equal distance to a detector station, and

means responsive to a phase difference between said beams at thedetector station for generating a signal proportional to the sense andmagnitude of said phase difference that varies in accordance with thechange in distance travelled by said beams as a result of movement ofthe housing with respect to the fixed reference.

2. A motion transducer as set forth in claim 1 wherein said superfiuidbath is liquid helium ll maintained at a temperature on the order of0.5K. to 22 K.

3. A motion transducer as set forth in claim 2 wherein said generatormeans is a carbon resistance heater located within said bath.

4. A system for measuring absolute rational motion comprising:

a container rotationally mounted with respect to a fixed reference,

a super cold liquid having a superfiuid component and a normal componentfilling said container, said superfluid component remaining at restbelow a critical angular velocity of said container,

generator means for producing an entropy wave in said super cold liquid,

a beam splitter at a wall of said container and movable therewith forsplitting said beam into two beams oppositely directed through saidsuper cold liquid, such that with the container in an at rest positionwith respect to the fixed reference, both beams travel substantially anequal distance to a detector station, and

means responsive to the phase difference between said oppositelydirected beams at the detector station for generating a signalproportional to the sense and magnitude of said phase difference thatvaries in accordance with the change in distance travelled by said beamsas a result of movement of the container with respect to the fixedreference.

5. A system for measuring absolute rotational motion as set forth inclaim 4 wherein said super cold liquid is liquid helium ll.

6. A system for measuring absolute rotational motion as set forth inclaim 4 including reflector means at said container wall for reflectingsaid oppositely directed beams through said bath to said detectorstation.

7. A system for measuring absolute rotational motion as set forth inclaim 6 including servo means responsive to said proportional signal forcontrolling the angular velocity of said container to maintain a phasenull between said oppositely directed beams at the detector station.

8. A system for measuring absolute rotational motion as set forth inclaim 7 wherein said servo means includes an amplifier responsive to thesense and magnitude of said proportional signal.

9. A system for measuring absolute rotational motion comprising:

a cylindrical container rotatably mounted with respect to a fixedreference,

liquid helium ll filling said container having a superfluid componentthat remains at a rest velocity below a critical angular velocity ofsaid container,

generator means for producing an entropy wave in said bath,

a beam splitter attached to said container for splitting said wave intotwo beams oppositely directed through said bath, such that with saidcontainer in an at rest position with respect to the fixed reference,both beams travel substantially an equal distance to a detector station,

reflector means attached to said cylindrical container for reflectingsaid oppositely directed beams from said beam splitter to the detectorstation, and

means responsive to the phase difference between said beams at thedetector station for generating a signal pro portional to the sense andmagnitude of said difference that varies in accordance with the changein distance travelled by said beams as a result of movement of saidcontainer with respect to the fixed reference.

10. A system for measuring absolute rotational motion as set forth inclaim 9 wherein said entropy wave generator is a shielded reslstanceheater producing a beam in a fixed direction.

11. A system for measuring absolute rotational motion as set forth inclaim 10 wherein said resistance heater is energized from a kHz. source.

12. A system for measuring absolute rotational motion as set forth inclaim 9 including servo means coupled to said cylindrical container andresponsive to said proportional signal to control the angular velocityof said container thereby maintaining a phase null between saidoppositely directed beams at said detector station.

13. A system for measuring absolute rotational motion as set forth inclaim 9 wherein said cylindrical container includes windows throughwhich said oppositely directed beams pass from said cylinder afterreflection from the detector station.

14. A method of measuring absolute rotational motion comprising thesteps of:

rotating a container of liquid helium ll with respect to a fixedreference,

generating an entropy wave in said. liquid helium II,

splitting said entropy wave into two beams oppositely directed throughsaid helium ll such that with the container in an at rest position bothbeams travel substantially an equal distance to a detector station, andgenerating a signal at the detector station proportional to the senseand magnitude of the phase difference between said oppositely directedbeams that varies in accordance with the change in path length travelledby said beams as a result of rotation of the container of liquid heliumll with respect to the fixed reference.

15. A method for measuring absolute rotational motion as set forth inclaim 14 including nulling said phase difference by controlling therotation of said container in response to said proportional signal.

16. A method of measuring absolute rotational motion as set forth inclaim 15 including the step of absorbing said oppositely directed beamsafter passing from said detector station.

CERTIFICATE OF CORRECTION Patent No.

Dated Au ust 2 1971 Invent fl Donald L. Enslev and that said Col Col

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line line line line

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It is certified that error appears in the above-identified patentLetters Patent are hereby corrected as shown below:

7D, =D D should be 8, "q =pstv should be --q =psTv 12, after "in" thefollowing was omitted: -the liquid helium is given by the equation:-;

23, point" should be --A point---;

23, "unit" should be unity;

35, }5- was omitted from beginning of Equation (5) 66, after "cm insertFor these parameters, th

critical angular velocity.

6, "dow 10" should be -dow 30-. 10, "rational" should be --r'otational.12, after "said" insert phase-.

Signed and sealed this 25th day of January 1972.

(SEAL) Attest:

EDWARD M.FLETCHER,JR. A't-testing Officer ROBERT GOTTSCHALK Commissionerof Patents

1. A motion transducer comprising: a superfluid bath within a housingpositionable with respect to a fixed reference, said bath having asuperfluid component that remains at rest below a critical velocity ofsaid housing, generator means for producing high frequency entropy wavesin said bath, reflector means for splitting said waves into two beamsoppositely directed through said bath, such that with the housing in anat rest position with respect to the fixed reference, both beams travelsubstantially an equal distance to a detector station, and meansresponsive to a phase difference between said beams at the detectorstation for generating a signal proportional to the sense and magnitudeof said phase difference that varies in accordance with the change indistance travelled by said beams as a result of movement of the housingwith respect to the fixed reference.
 2. A motion transducer as set forthin claim 1 wherein said superfluid bath is liquid helium II maintainedat a temperature on the order of 0.5* K. to 2.2* K.
 3. A motiontransducer as set forth in claim 2 wherein said generator means is acarbon resistance heater located within said bath.
 4. A system formeasuring absolute rational motion comprising: a container rotationallymounted with respect to a fixed reference, a super cold liquid having asuperfluid component and a normal component filling said container, saidsuperfluid component remaining at rest below a critical angular velocityof said container, generator means for producing an entropy wave in saidsuper cold liquid, a beam splitter at a wall of said container andmovable therewith for splitting said beam into two beams oppositelydirected through said super cold liquid, such that with the container inan at rest position with respect to the fixed reference, both beamstravel substantially an equal distance to a detector station, and meansresponsive to the phase difference between said oppositely directedbeams at the detector station for generating a signal proportional tothe sense and magnitude of said phase difference that varies inaccordance with the change in distance travelled by said beams as aresult of movement of the container with respect to the fixed reference.5. A system for measuring absolute rotational motion as set forth inclaim 4 wherein said super cold liquid is liquid helium II.
 6. A systemfor measuring absolute rotational motion as set forth in claim 4including reflector means at said container wall for reflecting saidoppositely directed beams through said bath to said detector station. 7.A system for measuring absolute rotational motion as set forth in claim6 including servo means responsive to said proportional signal forcontrolling the angular velocity of said container to maintain a phasenull between said oppositely directed beams at the detector station. 8.A system for measuring absolute rotational motion as set forth in claim7 wherein said servo means includes an amplifier responsive to the senseand magnitude of said proportional signal.
 9. A system for measuringabsolute rotational motion comprising: a cylindrical container rotatablymounted with respect to a fixed reference, liquid helium II filling saidcontainer having a superfluid component that remains at a rest velocitybelow a critical angular velocity of said container, generator means forproducing an entropy wave in said bath, a beam splitter attached to saidcontainer for splitting said wave into two beams oppositely directedthrough said bath, such that with said container in an at rest positionwith respect to the fixed reference, both beams travel substantially anequal distance to a detector station, reflector means attached to saidcylindrical container for reflecting said oppositely directed beams fromsaid beam splitter to the detector station, and means responsive to thephase difference between said beams at the detector station forgenerating a signal proportional to the sense and magnitude of saiddifference that varies in accordance with the change in distancetravelled by said beams as a result of movement of said container withrespect to the fixed reference.
 10. A system for measuring absoluterotational motion as set forth in claim 9 wherein said entropy wavegenerator is a shielded resistance heater producing a beam in a fixeddirection.
 11. A system for measuring absolute rotational motion as setforth in claim 10 wherein said resistance heater is energized from a 100kHz. source.
 12. A system for measuring absolute rotational motion asset forth in claim 9 including servo means coupled to said cylindricalcontainer and responsive to said proportional signal to control theangular velocity of said container thereby maintaining a phase nullbetween said oppositely directed beams at said detector station.
 13. Asystem for measuring absolute rotational motion as set forth in claim 9wherein said cylindrical container includes windows through which saidoppositely directed beams pass from said cylinder after reflection fromthe detector station.
 14. A method of measuring absolute rotationalmotion comprising the steps of: rotating a container of liquid helium IIwith respect to a fixed reference, generating an entropy wave in saidliquid helium II, splitting said entropy wave into two beams oppositelydirected through said helium II such that with the container in an atrest position both beams travel substantially an equal distance to adetector station, and generating a signal at the detector stationproportional to the sense and magnitude of the phase difference betweensaid oppositely directed beams that varies in accordance with the changein path length travelled by said beams as a result of rotation of thecontainer of liquid helium II with respect to the fixed reference.
 15. Amethod for measuring absolute rotational motion as set forth in claim 14including nulling said phase difference by controlling the rotation ofsaid container in response to said proportional signal.
 16. A method ofmeasuring absolute rotational motion as set forth in claim 15 includingthe step of absorbing said oppositely directed beams after passing fromsaid detector station.